Relative noise

ABSTRACT

Relative noise is a single scalar value that is used to predict the maximum value of the expected noise at any point and is calculated from the measured signal and a mathematical noise model. The mathematical noise model is selected or estimated from an observation that includes statistical and/or numerical modeling based on a population of measurement points. An absolute noise for a plurality of points of the measured signal is estimated. An array of values is calculated by dividing each of a plurality of points of the absolute noise by a corresponding expected noise value calculated from the mathematical noise model. The relative noise is calculated by taking a standard deviation of a plurality of points of the array. The relative noise can be used to calculate scaled background signal noise, filter regions, denoise data, detect false positives from features, calculate S/N, and determine a stop condition for acquiring data.

INTRODUCTION

Determining whether or not a given data point is significant is a commonproblem in data processing. A mass spectrometry data point, for example,is significant if it can be attributed to a real peak rather than theunderlying background signal plus noise. Generally a data point that islarge compared to the expected noise is significant. However, such acomparison is more difficult as the noise gets larger or the data pointgets smaller. Such a comparison is also difficult in regions where thereare few or no data points adjacent to the data point of interest. Inthese regions, there are too few data points to accurately model theexpected noise.

DRAWINGS

The skilled person in the art will understand that the drawings,described below, are for illustration purposes only. The drawings arenot intended to limit the scope of the applicant's teachings in any way.

FIG. 1 is a block diagram that illustrates a computer system, upon whichembodiments of the present teachings may be implemented.

FIG. 2 is a flowchart showing a method for calculating the relativenoise of a measured signal, in accordance with the present teachings.

Before one or more embodiments of the invention are described in detail,one skilled in the art will appreciate that the invention is not limitedin its application to the details of construction, the arrangements ofcomponents, and the arrangement of steps set forth in the followingdetailed description or illustrated in the drawings. The invention iscapable of other embodiments and of being practiced or being carried outin various ways. Also, it is to be understood that the phraseology andterminology used herein is for the purpose of description and should notbe regarded as limiting.

DESCRIPTION OF VARIOUS EMBODIMENTS

The section headings used herein are for organizational purposes onlyand are not to be construed as limiting the subject matter described inany way. Embodiments of systems and methods related to relative noiseare described in this detailed description.

Computer Implemented System

FIG. 1 is a block diagram that illustrates a computer system 100, uponwhich embodiments of the present teachings may be implemented. Computersystem 100 includes a bus 102 or other communication mechanism forcommunicating information, and a processor 104 coupled with bus 102 forprocessing information. Computer system 100 also includes a memory 106,which can be a random access memory (RAM) or other dynamic storagedevice, coupled to bus 102 for determining base calls, and instructionsto be executed by processor 104. Memory 106 also may be used for storingtemporary variables or other intermediate information during executionof instructions to be executed by processor 104. Computer system 100further includes a read only memory (ROM) 108 or other static storagedevice coupled to bus 102 for storing static information andinstructions for processor 104. A storage device 110, such as a magneticdisk or optical disk, is provided and coupled to bus 102 for storinginformation and instructions.

Computer system 100 may be coupled via bus 102 to a display 112, such asa cathode ray tube (CRT) or liquid crystal display (LCD), for displayinginformation to a computer user. An input device 114, includingalphanumeric and other keys, is coupled to bus 102 for communicatinginformation and command selections to processor 104. Another type ofuser input device is cursor control 116, such as a mouse, a trackball orcursor direction keys for communicating direction information andcommand selections to processor 104 and for controlling cursor movementon display 112. This input device typically has two degrees of freedomin two axes, a first axis (e.g., x) and a second axis (e.g., y), thatallows the device to specify positions in a plane.

A computer system 100 can perform the present teachings. Consistent withcertain implementations of the present teachings, results are providedby computer system 100 in response to processor 104 executing one ormore sequences of one or more instructions contained in memory 106. Suchinstructions may be read into memory 106 from another computer-readablemedium, such as storage device 110. Execution of the sequences ofinstructions contained in memory 106 causes processor 104 to perform theprocess described herein. Alternatively hard-wired circuitry may be usedin place of or in combination with software instructions to implementthe present teachings. Thus implementations of the present teachings arenot limited to any specific combination of hardware circuitry andsoftware.

The term “computer-readable medium” as used herein refers to any mediathat participates in providing instructions to processor 104 forexecution. Such a medium may take many forms, including but not limitedto, non-volatile media, volatile media, and transmission media.Non-volatile media includes, for example, optical or magnetic disks,such as storage device 110. Volatile media includes dynamic memory, suchas memory 106. Transmission media includes coaxial cables, copper wire,and fiber optics, including the wires that comprise bus 102.Transmission media can also take the form of acoustic or light waves,such as those generated during radio-wave and infra-red datacommunications.

Common forms of computer-readable media include, for example, a floppydisk, a flexible disk, hard disk, magnetic tape, or any other magneticmedium, a CD-ROM, any other optical medium, punch cards, papertape, anyother physical medium with patterns of holes, a RAM, PROM, and EPROM, aFLASH-EPROM, any other memory chip or cartridge, a carrier wave asdescribed hereinafter, or any other medium from which a computer canread.

Various forms of computer-readable media may be involved in carrying oneor more sequences of one or more instructions to processor 104 forexecution. For example, the instructions may initially be carried on themagnetic disk of a remote computer. The remote computer can load theinstructions into its dynamic memory and send the instructions over atelephone line using a modem. A modem local to computer system 100 canreceive the data on the telephone line and use an infra-red transmitterto convert the data to an infra-red signal. An infra-red detectorcoupled to bus 102 can receive the data carried in the infra-red signaland place the data on bus 102. Bus 102 carries the data to memory 106,from which processor 104 retrieves and executes the instructions. Theinstructions received by memory 106 may optionally be stored on storagedevice 110 either before or after execution by processor 104.

In accordance with various embodiments, instructions configured to beexecuted by a processor to perform a method are stored on acomputer-readable medium. The computer-readable medium can be a devicethat stores digital information. For example, a computer-readable mediumcan include, but is not limited to, a compact disc read-only memory(CD-ROM) as is known in the art for storing software. Thecomputer-readable medium is accessed by a processor suitable forexecuting instructions configured to be executed.

The following descriptions of various implementations of the presentteachings have been presented for purposes of illustration anddescription. It is not exhaustive and does not limit the presentteachings to the precise form disclosed. Modifications and variationsare possible in light of the above teachings or may be acquired frompracticing of the present teachings. Additionally, the describedimplementation includes software but the present teachings may beimplemented as a combination of hardware and software or in hardwarealone. The present teachings may be implemented with bothobject-oriented and non-object-oriented programming systems.

Methods of Data Processing

One method for determining the significance of a data point includesmeasuring the signal-to-noise ratio (S/N). Measuring the S/N works wellwhen the measured signal is large compared to the measured or estimatednoise. Measuring the S/N becomes more difficult as the noise gets largeror the measured signal gets smaller. Also, measuring the S/N todetermine the significance of a data point becomes more difficult if thenoise changes across the data or depends on the data in some way.

In various embodiments, a measured signal from a mass spectrometer, forexample, can include an underlying signal and an absolute noise. Theunderlying signal, in turn, can include a background signal and thesignal of interest. The underlying signal can be, for example, thesignal produced by a sample. The background signal can be, for example,a signal component of the underlying signal that has no information thatis characteristic of the sample. Such a background signal is, therefore,uninteresting from a biological or chemical point of view. In variousembodiments, the background signal can be mostly ion source dependantand independent variable (mass to charge ratio (m/z) or time) dependant.The signal of interest can be, for example, one or more signalcomponents of the underlying signal that carry significant informationabout the sample. The absolute noise of the measured signal, therefore,can include background noise from the background signal and noise fromthe signal of interest.

In various embodiments, the noise of a mass spectrometer can depend onthe data. For example, if the mass spectrometer is modeled as a pulsecounting system, the noise can be governed by Poisson statistics. As aresult, the variance of the data is the same as its mean, so thestandard deviation, and hence some part of the noise, is calculated fromthe square root of the mean of the data. In other words, the noise of amass spectrometer can be estimated from a mathematical noise model thatdepends on the square root of the signal intensity. Using thismathematical noise model, it is possible to calculate the expected noisefrom one known point of interest (signal intensity) of the measuredsignal.

In various embodiments, a single scalar value can be used to predict theexpected noise range at any point in the data. This expected noise canthen be compared to a measured signal or an underlying signal todetermine the significance of the signal. The single scalar value thatcan be used is called relative noise, for example.

FIG. 2 is a flowchart showing a method 200 for calculating the relativenoise of a measured signal, in accordance with the present teachings.

In step 210 of method 200, a mathematical noise model is selected. Themathematical noise model can be selected, for example, based onknowledge about a data acquisition process of the measured signal. Invarious embodiments, the mathematical noise model can be selected basedon an observation made from the measured signal. The observation caninclude, for example, statistical and/or numerical modeling based on apopulation of measurement points.

In step 220, an absolute noise for a plurality of points of the measuredsignal is estimated. The absolute noise can be estimated, for example,by subtracting an estimate of an underlying signal from the measuredsignal. An estimate of the underlying signal can be obtained, forexample, by smoothing the measured signal. In various embodiments, anestimate of the underlying signal can be obtained by applying a noisefilter to the measured signal.

In various embodiments, the absolute noise can be estimated by applyinga filter to the measured signal. The underlying signal can then beestimated by subtracting the estimated absolute noise from the measuredsignal.

In step 230, an array of values is calculated by dividing each of aplurality of points of the absolute noise by a corresponding expectednoise value calculated from the mathematical noise model.

In step 240, the relative noise is calculated by taking a standarddeviation of a plurality of points of the array.

In various embodiments, a computer system is used to calculate therelative noise of a measured signal. The computer system can be, but isnot limited to, computer system 100, shown in FIG. 1 and describedabove. The computer system includes a processor. The processor selects amathematical noise model. The processor estimates an absolute noise fora plurality of points of the measured signal. The processor calculatesan array of values by dividing each of a plurality of points of theabsolute noise by a corresponding expected noise value calculated fromthe mathematical noise model. Finally, the processor calculates therelative noise by taking a standard deviation of a plurality of pointsof the array.

In various embodiments, the relative noise can be used to calculate ascaled noise. An expected noise is predicted using the mathematicalnoise model and a signal. The signal can be a one-dimensional signal ora two-dimensional signal, for example. The signal can be, but is notlimited to, a background signal, an underlying signal, a signal ofinterest, or the measured signal. The background signal, underlyingsignal, and signal of interest can be estimated, for example. The scalednoise is calculated by multiplying the expected noise by the relativenoise. The signal and the scaled noise can be used in a number ofapplications.

EXAMPLES

Aspects of the applicant's teachings may be further understood in lightof the following examples, which should not be construed as limiting thescope of the present teachings in any way.

In various embodiments, the relative noise can be used to determine if aregion of a signal includes a signal of interest. A region of a signal,for example, includes one or more neighboring sampling points of thesignal. The signal can be the measured signal or the underlying signal,for example. As described above, the relative noise can be used tocalculate a scaled background signal noise. The sum of the scaledbackground signal noise in the region and the estimated backgroundsignal in the region is compared with the signal in the region. If thesignal in the region is greater than this sum, the region is determinedto include a signal of interest.

In various embodiments, the relative noise can be used to determine iftwo features of a signal overlap and should be analyzed together. Thetwo features of the signal are, for example, a first feature and asecond feature. The first feature and the second feature are adjacentfeatures, for example. A point of the signal that is between the firstfeature and the second feature is selected. The sum of a backgroundsignal value at the point and a scaled background signal noise value atthe point is compared with the signal value at the point. If the signalvalue at the point is greater than the sum at the point, then the firstfeature and the second feature overlap and are analyzed together.

In various embodiments, a feature can include a group of neighboringdata points in the signal. The signal can include one-dimensional andtwo-dimensional data. For example, the signal can include, but is notlimited to, liquid chromatography mass spectrometry (LCMS) data, imagedata, a mass spectrum, or a chromatogram.

In various embodiments, the relative noise can be used to determine if asecond feature of a signal is a real, separate feature and not part offirst feature of the signal. A first feature signal is estimated usingthe first feature, the signal, and a mathematical model for a feature.An expected first feature noise is predicted using the mathematicalnoise model, the first feature signal and the background signal. Ascaled first feature noise is calculated by multiplying the expectedfirst feature noise by the relative noise. The sum of a backgroundsignal value at the second feature, a first feature signal value at thesecond feature, and a scaled first feature noise value at the secondfeature is compared with a signal value at the second feature. If thesignal value is greater than the sum, the second feature is determinedto be the real, separate feature. If the signal value is not greaterthan the sum, the second feature is a false positive, for example.

In various embodiments, the relative noise can be used to denoise apoint of a signal. Denoising data involves decreasing data points likelyto be noise, while leaving data points less likely to be noiseunchanged. Those data points most likely to be noise are decreased themost. A scaled background signal noise value at a point of the signal iscompared with the difference between the signal value at the point and abackground signal value at the point. If the difference is smaller thanthe scaled background signal noise value, a value of zero is assigned tothe point. If the difference exceeds the scaled background signal noisevalue by a value greater than zero but less than a threshold, theproduct of the difference and a multiplier is assigned to the point. Themultiplier is, for example, a scalar value between zero and one. If thedifference exceeds the scaled background signal noise value by a valuegreater than or equal to the threshold, the difference is assigned tothe point.

In various embodiments, relative noise can be used to calculate thenoise component for a calculation of the S/N. The S/N at a point of asignal is calculated by dividing the difference between a signal valueat the point and a background signal value at the point by a product ofthe relative noise and a noise value at the point. The noise value canbe, but is not limited to, a background signal noise value or anunderlying signal noise value.

In various embodiments, the S/N at a point of the measured signal can beused to determine a stop condition for acquiring the measured signal. Ifthe S/N is greater than or equal to a threshold S/N, acquisition of themeasured signal is stopped.

In various embodiments, the relative noise of the measured signal can beused to determine a stop condition for acquiring the measured signal. Ifthe relative noise is less than or equal to a threshold value,acquisition of the measured signal is stopped. The relative noise canget smaller and smaller as the length of data acquisition of themeasured signal increases. In mass spectroscopy, longer data acquisitioncan imply that more spectra are averaged. If there is no signal ofinterest on top of the background signal, the measured signal or theunderlying signal does not increase no matter how long data is acquired.However, the relative noise can continue to decrease, because thebackground signal can get smoother and smoother.

While the applicants' teachings are described in conjunction withvarious embodiments, it is not intended that the applicants' teachingsbe limited to such embodiments. On the contrary, the applicants'teachings encompass various alternatives, modifications, andequivalents, as will be appreciated by those of skill in the art.

Further, in describing various embodiments, the specification may havepresented a method and/or process as a particular sequence of steps.However, to the extent that the method or process does not rely on theparticular order of steps set forth herein, the method or process shouldnot be limited to the particular sequence of steps described. As one ofordinary skill in the art would appreciate, other sequences of steps maybe possible. Therefore, the particular order of the steps set forth inthe specification should not be construed as limitations on the claims.In addition, the claims directed to the method and/or process should notbe limited to the performance of their steps in the order written, andone skilled in the art can readily appreciate that the sequences may bevaried and still remain within the spirit and scope of the variousembodiments.

What is claimed is:
 1. A method for calculating a relative noise of ameasured signal, comprising: selecting a mathematical noise model;estimating an absolute noise for a plurality of points of the measuredsignal; calculating a plurality of expected noise values from themathematical noise model for each of the plurality of points;calculating an array of values by dividing each of a plurality of pointsof the absolute noise by a corresponding expected noise value from theplurality of expected noise values; and calculating the relative noiseby taking a standard deviation of a plurality of points of the array. 2.The method of claim 1, wherein the mathematical noise model is selectedbased on knowledge about a data acquisition process of the measuredsignal.
 3. The method of claim 1, wherein the mathematical noise modelis selected based on an observation made from the measured signal. 4.The method of claim 1, further comprising estimating an underlyingsignal from the measured signal.
 5. The method of claim 4, wherein theabsolute noise is estimated by subtracting the underlying signal fromthe measured signal.
 6. The method of claim 4, wherein the underlyingsignal is obtained by smoothing the measured signal.
 7. The method ofclaim 4, wherein the underlying signal is obtained by applying a noisefilter to the measured signal.
 8. The method of claim 1, wherein theabsolute noise is estimated by applying a filter to the measured signal.9. The method of claim 8, wherein an underlying signal is estimated bysubtracting the absolute noise from the measured signal.
 10. The methodof claim 1, further comprising: predicting an expected noise using themathematical noise model and a signal; and calculating a scaled noise bymultiplying the expected noise by the relative noise.
 11. The method ofclaim 10, wherein the signal comprises an underlying signal.
 12. Themethod of claim 10, wherein the signal comprises a signal of interest.13. The method of claim 10, wherein the signal comprises the measuredsignal.
 14. The method of claim 1, further comprising: estimating abackground signal; predicting an expected background signal noise usingthe mathematical noise model and the background signal; and calculatinga scaled background signal noise by multiplying the expected backgroundsignal noise by the relative noise.
 15. The method of claim 14, furthercomprising determining if a region of a signal includes a signal ofinterest by: comparing a sum of a background signal value of thebackground signal in the region and a scaled background signal noisevalue of the scaled background signal noise in the region with a signalvalue of the signal in the region; and if the signal value is greaterthan the sum, determining that the region comprises the signal ofinterest.
 16. The method of claim 15, wherein the signal comprises themeasured signal.
 17. The method of claim 15, wherein the signalcomprises an underlying signal.
 18. The method of claim 14, furthercomprising determining if a first feature of a signal and an adjacentsecond feature of the signal are analyzed together by: selecting a pointof the signal that is between the first feature and the second feature;comparing a sum of a background signal value of the background signal atthe point and a scaled background signal noise value of the scaledbackground signal noise at the point with a signal value of the signalat the point; and if the signal value is greater than the sum, analyzingthe first feature and the second feature together.
 19. The method ofclaim 18, wherein the first feature comprises a first group ofneighboring data points in the signal and the second feature comprises asecond group of neighboring data points in the signal.
 20. The method ofclaim 18, wherein the signal comprises liquid chromatography massspectrometry data.
 21. The method of claim 18, wherein the signalcomprises image data.
 22. The method of claim 18, wherein the signalcomprises a mass spectrum.
 23. The method of claim 18, wherein thesignal comprises a chromatogram.
 24. The method of claim 18, wherein thesignal comprises the measured signal.
 25. The method of claim 18,wherein the signal comprises an underlying signal.
 26. The method ofclaim 14, further comprising determining if a second feature of a signalis a separate feature and not part of an adjacent first feature of thesignal by: estimating a first feature signal using the first feature,the signal, and a mathematical model for a feature; predicting anexpected first feature noise using the mathematical noise model, thefirst feature signal, and the background signal; calculating a scaledfirst feature noise by multiplying the expected first feature noise bythe relative noise; comparing a sum of a background signal value of thebackground signal at the second feature, a first feature signal value ofthe first feature signal at the second feature, and a scaled firstfeature noise value of the scaled first feature noise at the secondfeature with a signal value of the signal at the second feature; and ifthe signal value is greater than the sum, determining that the secondfeature comprises the separate feature.
 27. The method of claim 26,wherein the signal comprises the measured signal.
 28. The method ofclaim 26, wherein the signal comprises an underlying signal.
 29. Themethod of claim 14, further comprising denoising a point of a signal by:comparing a scaled background signal noise value of the scaledbackground signal noise at the point with a difference between a signalvalue of the signal at the point and a background signal value of thebackground signal at the point; if the difference is smaller than thescaled background signal noise value, assigning a value of zero to thepoint; if the difference exceeds the scaled background signal noisevalue by a value greater than zero but less than a threshold, assigninga product of the difference and a multiplier to the point; and if thedifference exceeds the scaled background signal noise value by a valuegreater than or equal to the threshold, assigning the difference to thepoint.
 30. The method of claim 29, wherein the signal comprises themeasured signal.
 31. The method of claim 29, wherein the signalcomprises an underlying signal.
 32. The method of claim 14, furthercomprising calculating a signal-to-noise ratio at a point of a signalby: dividing a difference between a signal value of the signal at thepoint and a background signal value of the background signal at thepoint by a product of the relative noise and a noise value at the point.33. The method of claim 32, wherein the noise value comprises anunderlying signal noise value.
 34. The method of claim 32, wherein thenoise value comprises a background signal noise value.
 35. The method ofclaim 32, further comprising: if the signal-to-noise ratio is greaterthan or equal to a threshold signal-to-noise ratio, stopping acquisitionof the measured signal.
 36. The method of claim 32, further comprising:if the relative noise is less than or equal to a thresholdsignal-to-noise ratio, stopping acquisition of the measured signal. 37.A non-transitory computer-readable medium containing computerinstructions stored therein, for calculating a relative noise of ameasured signal, causing a computer processor to perform: selecting amathematical noise model; estimating an absolute noise for a pluralityof points of the measured signal; calculating a plurality of expectednoise values from the mathematical noise model for each of the pluralityof points; calculating an array of values by dividing each of aplurality of points of the absolute noise by a corresponding expectednoise value from the plurality of expected noise values; and calculatingthe relative noise by taking a standard deviation of a plurality ofpoints of the array.
 38. A computing system for calculating a relativenoise of a measured signal, comprising: a computer processor programmedto calculate the relative noise of the measured signal that, whenexecuted by the computer processor: selects a mathematical noise model,estimates an absolute noise for a plurality of points of the measuredsignal, calculates a plurality of expected noise values from themathematical noise model for each of the plurality of points, calculatesan array of values by dividing each of a plurality of points of theabsolute noise by a corresponding expected noise value from theplurality of expected noise values, and calculates the relative noise bytaking a standard deviation of a plurality of points of the array.